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Popular Calculus Problems

integral of-0.6x^2+80	\int\:-0.6x^{2}+80dx
derivative of sqrt(1+2x)	derivative\:\sqrt{1+2x}
integral of 1/(t^2-1)	\int\:\frac{1}{t^{2}-1}dt
derivative of x^2+(y^2/9)=1	\frac{d}{dx}(x^{2}+\frac{y^{2}}{9})=1
laplacetransform t^{3/2}	laplacetransform\:t^{\frac{3}{2}}
area y= 3/2 x,y=7-x^2	area\:y=\frac{3}{2}x,y=7-x^{2}
integral of t/(\sqrt[3]{t^2+9)}	\int\:\frac{t}{\sqrt[3]{t^{2}+9}}dt
y^'=8y^2	y^{\prime\:}=8y^{2}
integral of tsec(t)tan(t)	\int\:t\sec(t)\tan(t)dt
integral from 2 to infinity of e^{-5p}	\int\:_{2}^{\infty\:}e^{-5p}dp
integral from 1 to 2 of 7/(x^3+5x)	\int\:_{1}^{2}\frac{7}{x^{3}+5x}dx
integral of xcos^2(6x)	\int\:x\cos^{2}(6x)dx
xln(x)y^'+y=8xe^x	x\ln(x)y^{\prime\:}+y=8xe^{x}
taylor x/(1-x^2)	taylor\:\frac{x}{1-x^{2}}
sum from n=0 to infinity of 1/(nln(n))	\sum\:_{n=0}^{\infty\:}\frac{1}{n\ln(n)}
(\partial)/(\partial x)(x^2y+2y^2-4xy+6)	\frac{\partial\:}{\partial\:x}(x^{2}y+2y^{2}-4xy+6)
integral of (y^2+20y+100)/((y^2+100)^2)	\int\:\frac{y^{2}+20y+100}{(y^{2}+100)^{2}}dy
y^{''}-8y^'+19y=0	y^{\prime\:\prime\:}-8y^{\prime\:}+19y=0
(\partial)/(\partial x)(1/(x^2+a^2))	\frac{\partial\:}{\partial\:x}(\frac{1}{x^{2}+a^{2}})
tangent of y=(x^3-25x)^{12},(-5,0)	tangent\:y=(x^{3}-25x)^{12},(-5,0)
integral of a+18	\int\:a+18
derivative of sin(7pix)	\frac{d}{dx}(\sin(7πx))
integral of-7e^{5x}	\int\:-7e^{5x}dx
integral from 0 to pi/(24) of cos(4x)	\int\:_{0}^{\frac{π}{24}}\cos(4x)dx
integral of sqrt(9+16t^2)	\int\:\sqrt{9+16t^{2}}dt
limit as x approaches 3 of (1-x)/(x-3)	\lim\:_{x\to\:3}(\frac{1-x}{x-3})
(\partial)/(\partial y)(x^2+2y)	\frac{\partial\:}{\partial\:y}(x^{2}+2y)
derivative of x^n(ln(x)^2)	\frac{d}{dx}(x^{n}(\ln(x))^{2})
derivative of f(x)=(9-xe^x)/(x+e^x)	derivative\:f(x)=\frac{9-xe^{x}}{x+e^{x}}
derivative of (5x-2^3)	\frac{d}{dx}((5x-2)^{3})
derivative of sin^2(pi-x)	\frac{d}{dx}(\sin^{2}(π-x))
(dy)/(dt)=(3t^2+te^{-t}+1)/(2y-4)	\frac{dy}{dt}=\frac{3t^{2}+te^{-t}+1}{2y-4}
integral of a/(x^2)	\int\:\frac{a}{x^{2}}dx
integral of 1/((x+3))	\int\:\frac{1}{(x+3)}dx
derivative of ((3-2x-x^2)/((x^2-1)))	\frac{d}{dx}(\frac{(3-2x-x^{2})}{(x^{2}-1)})
(dy)/(dt)=y*ln(t),y(e)=200	\frac{dy}{dt}=y\cdot\:\ln(t),y(e)=200
limit as x approaches 2 of (-x)/((2-x))	\lim\:_{x\to\:2}(\frac{-x}{(2-x)})
integral of e^{x+7e^x}	\int\:e^{x+7e^{x}}dx
derivative of sqrt(3x^2-4)	\frac{d}{dx}(\sqrt{3x^{2}-4})
integral of-2/3 (1-x)^{3/2}(1)	\int\:-\frac{2}{3}(1-x)^{\frac{3}{2}}(1)dx
y^{''}+25y=sec(5x)	y^{\prime\:\prime\:}+25y=\sec(5x)
integral of p	\int\:pdp
(d^2y)/(dx^2)-4(dy)/(dx)+68y=0	\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+68y=0
limit as x approaches-7-of (-9x)/(x+7)	\lim\:_{x\to\:-7-}(\frac{-9x}{x+7})
integral of (x+3)/(sqrt(x))	\int\:\frac{x+3}{\sqrt{x}}dx
limit as x approaches 4 of sqrt(25-x^2)	\lim\:_{x\to\:4}(\sqrt{25-x^{2}})
limit as x approaches 0 of (x+1)^2-x^2	\lim\:_{x\to\:0}((x+1)^{2}-x^{2})
(\partial)/(\partial x)(x^8+xy^5+5)	\frac{\partial\:}{\partial\:x}(x^{8}+xy^{5}+5)
derivative of y=2(6x^9-10x+4)^{-3}	derivative\:y=2(6x^{9}-10x+4)^{-3}
limit as x approaches infinity of e^3	\lim\:_{x\to\:\infty\:}(e^{3})
derivative of f(x)=(x+1/x)^5	derivative\:f(x)=(x+\frac{1}{x})^{5}
integral from 30 to 150 of (75)/(2x^2)	\int\:_{30}^{150}\frac{75}{2x^{2}}dx
inverse oflaplace (s-5)/(s^2+s-6)	inverselaplace\:\frac{s-5}{s^{2}+s-6}
derivative of sin(xdx)	\frac{d}{dx}(\sin(x)dx)
integral of xsqrt(3x-2)	\int\:x\sqrt{3x-2}dx
derivative of (3x^{ln(3x)})	\frac{d}{dx}((3x)^{\ln(3x)})
integral of sin^{-3/2}(x)cos^3(x)	\int\:\sin^{-\frac{3}{2}}(x)\cos^{3}(x)dx
limit as x approaches-1 of 2x^2-5x+3	\lim\:_{x\to\:-1}(2x^{2}-5x+3)
integral of 1/(4+t)	\int\:\frac{1}{4+t}dt
integral of xe^{10x}	\int\:xe^{10x}dx
limit as x approaches-b of (((x+b)^7+(x+b)^{10}))/(4(x+b))	\lim\:_{x\to\:-b}(\frac{((x+b)^{7}+(x+b)^{10})}{4(x+b)})
(\partial)/(\partial x)((x+y)^2+(x+1)^2)	\frac{\partial\:}{\partial\:x}((x+y)^{2}+(x+1)^{2})
integral of 1/2 sin^2(x)	\int\:\frac{1}{2}\sin^{2}(x)dx
(\partial)/(\partial x)(x+y^2)	\frac{\partial\:}{\partial\:x}(x+y^{2})
inverse oflaplace 3/(s^2+6s+10)	inverselaplace\:\frac{3}{s^{2}+6s+10}
derivative of 2cos^3(t)	derivative\:2\cos^{3}(t)
integral of e^{1/3 x}	\int\:e^{\frac{1}{3}x}dx
limit as x approaches-2+of sqrt(x+2)	\lim\:_{x\to\:-2+}(\sqrt{x+2})
derivative of x/(1-ln(x-1))	\frac{d}{dx}(\frac{x}{1-\ln(x-1)})
tangent of f(x)=2+4x^2,(0,2)	tangent\:f(x)=2+4x^{2},(0,2)
tangent of y= 8/(sin(x)+cos(x)),(0,8)	tangent\:y=\frac{8}{\sin(x)+\cos(x)},(0,8)
(\partial)/(\partial x)((3x-y)/(x+2y))	\frac{\partial\:}{\partial\:x}(\frac{3x-y}{x+2y})
integral of (cos(x))/(sin(x)+sin^2(x))	\int\:\frac{\cos(x)}{\sin(x)+\sin^{2}(x)}dx
y^{''}+34y=0	y^{\prime\:\prime\:}+34y=0
dx+dye^{6x}=0	dx+dye^{6x}=0
derivative of f(x)=e^1	derivative\:f(x)=e^{1}
integral of 4-4x^2	\int\:4-4x^{2}dx
area \|x-9\|, x/2	area\:\left\|x-9\right\|,\frac{x}{2}
y^{''}+5y^'+4y=-13te^{5t}	y^{\prime\:\prime\:}+5y^{\prime\:}+4y=-13te^{5t}
integral from 4 to x^2 of 3sqrt(1+t^2)	\int\:_{4}^{x^{2}}3\sqrt{1+t^{2}}dt
(dy)/(dx)-y=x	\frac{dy}{dx}-y=x
y^{''}+9y=tsin(3t)	y^{\prime\:\prime\:}+9y=t\sin(3t)
derivative of sec^{11}(x)	\frac{d}{dx}(\sec^{11}(x))
sum from n=0 to infinity of 6(0.9)^{n-1}	\sum\:_{n=0}^{\infty\:}6(0.9)^{n-1}
derivative of (x^2-5x+3^4)	\frac{d}{dx}((x^{2}-5x+3)^{4})
integral from-3 to 3 of \|x\|	\int\:_{-3}^{3}\left\|x\right\|dx
integral of (4e^{2x})/(e^{2x)+12e^x+32}	\int\:\frac{4e^{2x}}{e^{2x}+12e^{x}+32}dx
integral of (2x^2-3x+4)/(2x-7)	\int\:\frac{2x^{2}-3x+4}{2x-7}dx
integral of (x^6-x^3+1)/(x^4+9x^2)	\int\:\frac{x^{6}-x^{3}+1}{x^{4}+9x^{2}}dx
limit as x approaches infinity of (log_{4}(x))/(log_{9)(x)}	\lim\:_{x\to\:\infty\:}(\frac{\log_{4}(x)}{\log_{9}(x)})
integral from 1 to 5 of sqrt(x-1)	\int\:_{1}^{5}\sqrt{x-1}dx
integral of 3/7 x^{-1/7}	\int\:\frac{3}{7}x^{-\frac{1}{7}}dx
derivative of (x^2-x/(1+3x^2))	\frac{d}{dx}(\frac{x^{2}-x}{1+3x^{2}})
sum from k=0 to infinity of k!2^kx^k	\sum\:_{k=0}^{\infty\:}k!2^{k}x^{k}
tangent of f(x)=-3cos(x),\at x= 3/4 pi	tangent\:f(x)=-3\cos(x),\at\:x=\frac{3}{4}π
integral from 0 to 1 of ((4t^3)/(1+t^4))	\int\:_{0}^{1}(\frac{4t^{3}}{1+t^{4}})dt
integral of ((x^2))/((3+4x-4x^2)^{3/2)}	\int\:\frac{(x^{2})}{(3+4x-4x^{2})^{\frac{3}{2}}}dx
slope of (0,-3),(2,0)	slope\:(0,-3),(2,0)
integral from 1 to sqrt(3 of)x3^{(x^2)}	\int\:_{1}^{\sqrt{3}}x3^{(x^{2})}dx
(dy)/(dx)=((2y+5)/(4x+9))^2	\frac{dy}{dx}=(\frac{2y+5}{4x+9})^{2}

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